The purpose of this paper is to explore and analyze the effectiveness of long period supplementary zone rules that can simultaneously increase chart sensitivity to small process drift and not significantly increase the false alarm rate.
A stable, on‐target process was simulated and drift induced into the process. The rates of drift varied from 0.03σ to .0003σ per subgroup measurement. A total of 613 different supplementary zone rules were implemented in conjunction with the three‐sigma limiting rule. For each combination, 100,000 observations were simulated and the effect on the false alarm rate and increase in chart sensitivity estimated. An effectiveness measure was developed to relate false alarm rate to chart sensitivity.
A total of 87 rules were uncovered which effectively detected a wide range of process drifts. When the increase in chart sensitivity is discounted by the false alarm rate, 13 rules increased chart sensitivity by over 10 percent. These rules were based on longer rather than shorter rule length.
The effective rules discovered form a nonlinear pattern in the space the examined rules define. This indicates a direction for future research outside the scope of this study. These rules are also easy to implement in existing Shewhart chart applications where the process drifts at an unknown rate.
While supplementary trend rules have been studied in the past, the extension to zone rules has not been made. This study begins to fill that void and indicates the direction for future efforts in the area.
